Properties of Triangles question bank (Maths)

Let $a,b$ and $c$ be the length of sides of a triangle $ABC$ such that $\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}$. If $r$ and $R$ are the radius of incircle and radius of circumcircle of the triangle $ABC$, respectively, then the value of $\frac{R}{r}$ is equal to

Let in a right angled triangle, the smallest angle be $\theta .$ If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then $\sin \theta$ is equal to: